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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.transform;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.io.Serializable;<a name="line.19"></a>
<FONT color="green">020</FONT>    import java.lang.reflect.Array;<a name="line.20"></a>
<FONT color="green">021</FONT>    <a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.analysis.FunctionUtils;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.analysis.UnivariateFunction;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.complex.Complex;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.MathIllegalArgumentException;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.exception.MathIllegalStateException;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.util.ArithmeticUtils;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math3.util.MathArrays;<a name="line.31"></a>
<FONT color="green">032</FONT>    <a name="line.32"></a>
<FONT color="green">033</FONT>    /**<a name="line.33"></a>
<FONT color="green">034</FONT>     * Implements the Fast Fourier Transform for transformation of one-dimensional<a name="line.34"></a>
<FONT color="green">035</FONT>     * real or complex data sets. For reference, see &lt;em&gt;Applied Numerical Linear<a name="line.35"></a>
<FONT color="green">036</FONT>     * Algebra&lt;/em&gt;, ISBN 0898713897, chapter 6.<a name="line.36"></a>
<FONT color="green">037</FONT>     * &lt;p&gt;<a name="line.37"></a>
<FONT color="green">038</FONT>     * There are several variants of the discrete Fourier transform, with various<a name="line.38"></a>
<FONT color="green">039</FONT>     * normalization conventions, which are specified by the parameter<a name="line.39"></a>
<FONT color="green">040</FONT>     * {@link DftNormalization}.<a name="line.40"></a>
<FONT color="green">041</FONT>     * &lt;p&gt;<a name="line.41"></a>
<FONT color="green">042</FONT>     * The current implementation of the discrete Fourier transform as a fast<a name="line.42"></a>
<FONT color="green">043</FONT>     * Fourier transform requires the length of the data set to be a power of 2.<a name="line.43"></a>
<FONT color="green">044</FONT>     * This greatly simplifies and speeds up the code. Users can pad the data with<a name="line.44"></a>
<FONT color="green">045</FONT>     * zeros to meet this requirement. There are other flavors of FFT, for<a name="line.45"></a>
<FONT color="green">046</FONT>     * reference, see S. Winograd,<a name="line.46"></a>
<FONT color="green">047</FONT>     * &lt;i&gt;On computing the discrete Fourier transform&lt;/i&gt;, Mathematics of<a name="line.47"></a>
<FONT color="green">048</FONT>     * Computation, 32 (1978), 175 - 199.<a name="line.48"></a>
<FONT color="green">049</FONT>     *<a name="line.49"></a>
<FONT color="green">050</FONT>     * @see DftNormalization<a name="line.50"></a>
<FONT color="green">051</FONT>     * @version $Id: FastFourierTransformer.java 1385310 2012-09-16 16:32:10Z tn $<a name="line.51"></a>
<FONT color="green">052</FONT>     * @since 1.2<a name="line.52"></a>
<FONT color="green">053</FONT>     */<a name="line.53"></a>
<FONT color="green">054</FONT>    public class FastFourierTransformer implements Serializable {<a name="line.54"></a>
<FONT color="green">055</FONT>    <a name="line.55"></a>
<FONT color="green">056</FONT>        /** Serializable version identifier. */<a name="line.56"></a>
<FONT color="green">057</FONT>        static final long serialVersionUID = 20120210L;<a name="line.57"></a>
<FONT color="green">058</FONT>    <a name="line.58"></a>
<FONT color="green">059</FONT>        /**<a name="line.59"></a>
<FONT color="green">060</FONT>         * {@code W_SUB_N_R[i]} is the real part of<a name="line.60"></a>
<FONT color="green">061</FONT>         * {@code exp(- 2 * i * pi / n)}:<a name="line.61"></a>
<FONT color="green">062</FONT>         * {@code W_SUB_N_R[i] = cos(2 * pi/ n)}, where {@code n = 2^i}.<a name="line.62"></a>
<FONT color="green">063</FONT>         */<a name="line.63"></a>
<FONT color="green">064</FONT>        private static final double[] W_SUB_N_R =<a name="line.64"></a>
<FONT color="green">065</FONT>                {  0x1.0p0, -0x1.0p0, 0x1.1a62633145c07p-54, 0x1.6a09e667f3bcdp-1<a name="line.65"></a>
<FONT color="green">066</FONT>                , 0x1.d906bcf328d46p-1, 0x1.f6297cff75cbp-1, 0x1.fd88da3d12526p-1, 0x1.ff621e3796d7ep-1<a name="line.66"></a>
<FONT color="green">067</FONT>                , 0x1.ffd886084cd0dp-1, 0x1.fff62169b92dbp-1, 0x1.fffd8858e8a92p-1, 0x1.ffff621621d02p-1<a name="line.67"></a>
<FONT color="green">068</FONT>                , 0x1.ffffd88586ee6p-1, 0x1.fffff62161a34p-1, 0x1.fffffd8858675p-1, 0x1.ffffff621619cp-1<a name="line.68"></a>
<FONT color="green">069</FONT>                , 0x1.ffffffd885867p-1, 0x1.fffffff62161ap-1, 0x1.fffffffd88586p-1, 0x1.ffffffff62162p-1<a name="line.69"></a>
<FONT color="green">070</FONT>                , 0x1.ffffffffd8858p-1, 0x1.fffffffff6216p-1, 0x1.fffffffffd886p-1, 0x1.ffffffffff621p-1<a name="line.70"></a>
<FONT color="green">071</FONT>                , 0x1.ffffffffffd88p-1, 0x1.fffffffffff62p-1, 0x1.fffffffffffd9p-1, 0x1.ffffffffffff6p-1<a name="line.71"></a>
<FONT color="green">072</FONT>                , 0x1.ffffffffffffep-1, 0x1.fffffffffffffp-1, 0x1.0p0, 0x1.0p0<a name="line.72"></a>
<FONT color="green">073</FONT>                , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0<a name="line.73"></a>
<FONT color="green">074</FONT>                , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0<a name="line.74"></a>
<FONT color="green">075</FONT>                , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0<a name="line.75"></a>
<FONT color="green">076</FONT>                , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0<a name="line.76"></a>
<FONT color="green">077</FONT>                , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0<a name="line.77"></a>
<FONT color="green">078</FONT>                , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0<a name="line.78"></a>
<FONT color="green">079</FONT>                , 0x1.0p0, 0x1.0p0, 0x1.0p0, 0x1.0p0<a name="line.79"></a>
<FONT color="green">080</FONT>                , 0x1.0p0, 0x1.0p0, 0x1.0p0 };<a name="line.80"></a>
<FONT color="green">081</FONT>    <a name="line.81"></a>
<FONT color="green">082</FONT>        /**<a name="line.82"></a>
<FONT color="green">083</FONT>         * {@code W_SUB_N_I[i]} is the imaginary part of<a name="line.83"></a>
<FONT color="green">084</FONT>         * {@code exp(- 2 * i * pi / n)}:<a name="line.84"></a>
<FONT color="green">085</FONT>         * {@code W_SUB_N_I[i] = -sin(2 * pi/ n)}, where {@code n = 2^i}.<a name="line.85"></a>
<FONT color="green">086</FONT>         */<a name="line.86"></a>
<FONT color="green">087</FONT>        private static final double[] W_SUB_N_I =<a name="line.87"></a>
<FONT color="green">088</FONT>                {  0x1.1a62633145c07p-52, -0x1.1a62633145c07p-53, -0x1.0p0, -0x1.6a09e667f3bccp-1<a name="line.88"></a>
<FONT color="green">089</FONT>                , -0x1.87de2a6aea963p-2, -0x1.8f8b83c69a60ap-3, -0x1.917a6bc29b42cp-4, -0x1.91f65f10dd814p-5<a name="line.89"></a>
<FONT color="green">090</FONT>                , -0x1.92155f7a3667ep-6, -0x1.921d1fcdec784p-7, -0x1.921f0fe670071p-8, -0x1.921f8becca4bap-9<a name="line.90"></a>
<FONT color="green">091</FONT>                , -0x1.921faaee6472dp-10, -0x1.921fb2aecb36p-11, -0x1.921fb49ee4ea6p-12, -0x1.921fb51aeb57bp-13<a name="line.91"></a>
<FONT color="green">092</FONT>                , -0x1.921fb539ecf31p-14, -0x1.921fb541ad59ep-15, -0x1.921fb5439d73ap-16, -0x1.921fb544197ap-17<a name="line.92"></a>
<FONT color="green">093</FONT>                , -0x1.921fb544387bap-18, -0x1.921fb544403c1p-19, -0x1.921fb544422c2p-20, -0x1.921fb54442a83p-21<a name="line.93"></a>
<FONT color="green">094</FONT>                , -0x1.921fb54442c73p-22, -0x1.921fb54442cefp-23, -0x1.921fb54442d0ep-24, -0x1.921fb54442d15p-25<a name="line.94"></a>
<FONT color="green">095</FONT>                , -0x1.921fb54442d17p-26, -0x1.921fb54442d18p-27, -0x1.921fb54442d18p-28, -0x1.921fb54442d18p-29<a name="line.95"></a>
<FONT color="green">096</FONT>                , -0x1.921fb54442d18p-30, -0x1.921fb54442d18p-31, -0x1.921fb54442d18p-32, -0x1.921fb54442d18p-33<a name="line.96"></a>
<FONT color="green">097</FONT>                , -0x1.921fb54442d18p-34, -0x1.921fb54442d18p-35, -0x1.921fb54442d18p-36, -0x1.921fb54442d18p-37<a name="line.97"></a>
<FONT color="green">098</FONT>                , -0x1.921fb54442d18p-38, -0x1.921fb54442d18p-39, -0x1.921fb54442d18p-40, -0x1.921fb54442d18p-41<a name="line.98"></a>
<FONT color="green">099</FONT>                , -0x1.921fb54442d18p-42, -0x1.921fb54442d18p-43, -0x1.921fb54442d18p-44, -0x1.921fb54442d18p-45<a name="line.99"></a>
<FONT color="green">100</FONT>                , -0x1.921fb54442d18p-46, -0x1.921fb54442d18p-47, -0x1.921fb54442d18p-48, -0x1.921fb54442d18p-49<a name="line.100"></a>
<FONT color="green">101</FONT>                , -0x1.921fb54442d18p-50, -0x1.921fb54442d18p-51, -0x1.921fb54442d18p-52, -0x1.921fb54442d18p-53<a name="line.101"></a>
<FONT color="green">102</FONT>                , -0x1.921fb54442d18p-54, -0x1.921fb54442d18p-55, -0x1.921fb54442d18p-56, -0x1.921fb54442d18p-57<a name="line.102"></a>
<FONT color="green">103</FONT>                , -0x1.921fb54442d18p-58, -0x1.921fb54442d18p-59, -0x1.921fb54442d18p-60 };<a name="line.103"></a>
<FONT color="green">104</FONT>    <a name="line.104"></a>
<FONT color="green">105</FONT>        /** The type of DFT to be performed. */<a name="line.105"></a>
<FONT color="green">106</FONT>        private final DftNormalization normalization;<a name="line.106"></a>
<FONT color="green">107</FONT>    <a name="line.107"></a>
<FONT color="green">108</FONT>        /**<a name="line.108"></a>
<FONT color="green">109</FONT>         * Creates a new instance of this class, with various normalization<a name="line.109"></a>
<FONT color="green">110</FONT>         * conventions.<a name="line.110"></a>
<FONT color="green">111</FONT>         *<a name="line.111"></a>
<FONT color="green">112</FONT>         * @param normalization the type of normalization to be applied to the<a name="line.112"></a>
<FONT color="green">113</FONT>         * transformed data<a name="line.113"></a>
<FONT color="green">114</FONT>         */<a name="line.114"></a>
<FONT color="green">115</FONT>        public FastFourierTransformer(final DftNormalization normalization) {<a name="line.115"></a>
<FONT color="green">116</FONT>            this.normalization = normalization;<a name="line.116"></a>
<FONT color="green">117</FONT>        }<a name="line.117"></a>
<FONT color="green">118</FONT>    <a name="line.118"></a>
<FONT color="green">119</FONT>        /**<a name="line.119"></a>
<FONT color="green">120</FONT>         * Performs identical index bit reversal shuffles on two arrays of identical<a name="line.120"></a>
<FONT color="green">121</FONT>         * size. Each element in the array is swapped with another element based on<a name="line.121"></a>
<FONT color="green">122</FONT>         * the bit-reversal of the index. For example, in an array with length 16,<a name="line.122"></a>
<FONT color="green">123</FONT>         * item at binary index 0011 (decimal 3) would be swapped with the item at<a name="line.123"></a>
<FONT color="green">124</FONT>         * binary index 1100 (decimal 12).<a name="line.124"></a>
<FONT color="green">125</FONT>         *<a name="line.125"></a>
<FONT color="green">126</FONT>         * @param a the first array to be shuffled<a name="line.126"></a>
<FONT color="green">127</FONT>         * @param b the second array to be shuffled<a name="line.127"></a>
<FONT color="green">128</FONT>         */<a name="line.128"></a>
<FONT color="green">129</FONT>        private static void bitReversalShuffle2(double[] a, double[] b) {<a name="line.129"></a>
<FONT color="green">130</FONT>            final int n = a.length;<a name="line.130"></a>
<FONT color="green">131</FONT>            assert b.length == n;<a name="line.131"></a>
<FONT color="green">132</FONT>            final int halfOfN = n &gt;&gt; 1;<a name="line.132"></a>
<FONT color="green">133</FONT>    <a name="line.133"></a>
<FONT color="green">134</FONT>            int j = 0;<a name="line.134"></a>
<FONT color="green">135</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.135"></a>
<FONT color="green">136</FONT>                if (i &lt; j) {<a name="line.136"></a>
<FONT color="green">137</FONT>                    // swap indices i &amp; j<a name="line.137"></a>
<FONT color="green">138</FONT>                    double temp = a[i];<a name="line.138"></a>
<FONT color="green">139</FONT>                    a[i] = a[j];<a name="line.139"></a>
<FONT color="green">140</FONT>                    a[j] = temp;<a name="line.140"></a>
<FONT color="green">141</FONT>    <a name="line.141"></a>
<FONT color="green">142</FONT>                    temp = b[i];<a name="line.142"></a>
<FONT color="green">143</FONT>                    b[i] = b[j];<a name="line.143"></a>
<FONT color="green">144</FONT>                    b[j] = temp;<a name="line.144"></a>
<FONT color="green">145</FONT>                }<a name="line.145"></a>
<FONT color="green">146</FONT>    <a name="line.146"></a>
<FONT color="green">147</FONT>                int k = halfOfN;<a name="line.147"></a>
<FONT color="green">148</FONT>                while (k &lt;= j &amp;&amp; k &gt; 0) {<a name="line.148"></a>
<FONT color="green">149</FONT>                    j -= k;<a name="line.149"></a>
<FONT color="green">150</FONT>                    k &gt;&gt;= 1;<a name="line.150"></a>
<FONT color="green">151</FONT>                }<a name="line.151"></a>
<FONT color="green">152</FONT>                j += k;<a name="line.152"></a>
<FONT color="green">153</FONT>            }<a name="line.153"></a>
<FONT color="green">154</FONT>        }<a name="line.154"></a>
<FONT color="green">155</FONT>    <a name="line.155"></a>
<FONT color="green">156</FONT>        /**<a name="line.156"></a>
<FONT color="green">157</FONT>         * Applies the proper normalization to the specified transformed data.<a name="line.157"></a>
<FONT color="green">158</FONT>         *<a name="line.158"></a>
<FONT color="green">159</FONT>         * @param dataRI the unscaled transformed data<a name="line.159"></a>
<FONT color="green">160</FONT>         * @param normalization the normalization to be applied<a name="line.160"></a>
<FONT color="green">161</FONT>         * @param type the type of transform (forward, inverse) which resulted in the specified data<a name="line.161"></a>
<FONT color="green">162</FONT>         */<a name="line.162"></a>
<FONT color="green">163</FONT>        private static void normalizeTransformedData(final double[][] dataRI,<a name="line.163"></a>
<FONT color="green">164</FONT>            final DftNormalization normalization, final TransformType type) {<a name="line.164"></a>
<FONT color="green">165</FONT>    <a name="line.165"></a>
<FONT color="green">166</FONT>            final double[] dataR = dataRI[0];<a name="line.166"></a>
<FONT color="green">167</FONT>            final double[] dataI = dataRI[1];<a name="line.167"></a>
<FONT color="green">168</FONT>            final int n = dataR.length;<a name="line.168"></a>
<FONT color="green">169</FONT>            assert dataI.length == n;<a name="line.169"></a>
<FONT color="green">170</FONT>    <a name="line.170"></a>
<FONT color="green">171</FONT>            switch (normalization) {<a name="line.171"></a>
<FONT color="green">172</FONT>                case STANDARD:<a name="line.172"></a>
<FONT color="green">173</FONT>                    if (type == TransformType.INVERSE) {<a name="line.173"></a>
<FONT color="green">174</FONT>                        final double scaleFactor = 1.0 / ((double) n);<a name="line.174"></a>
<FONT color="green">175</FONT>                        for (int i = 0; i &lt; n; i++) {<a name="line.175"></a>
<FONT color="green">176</FONT>                            dataR[i] *= scaleFactor;<a name="line.176"></a>
<FONT color="green">177</FONT>                            dataI[i] *= scaleFactor;<a name="line.177"></a>
<FONT color="green">178</FONT>                        }<a name="line.178"></a>
<FONT color="green">179</FONT>                    }<a name="line.179"></a>
<FONT color="green">180</FONT>                    break;<a name="line.180"></a>
<FONT color="green">181</FONT>                case UNITARY:<a name="line.181"></a>
<FONT color="green">182</FONT>                    final double scaleFactor = 1.0 / FastMath.sqrt(n);<a name="line.182"></a>
<FONT color="green">183</FONT>                    for (int i = 0; i &lt; n; i++) {<a name="line.183"></a>
<FONT color="green">184</FONT>                        dataR[i] *= scaleFactor;<a name="line.184"></a>
<FONT color="green">185</FONT>                        dataI[i] *= scaleFactor;<a name="line.185"></a>
<FONT color="green">186</FONT>                    }<a name="line.186"></a>
<FONT color="green">187</FONT>                    break;<a name="line.187"></a>
<FONT color="green">188</FONT>                default:<a name="line.188"></a>
<FONT color="green">189</FONT>                    /*<a name="line.189"></a>
<FONT color="green">190</FONT>                     * This should never occur in normal conditions. However this<a name="line.190"></a>
<FONT color="green">191</FONT>                     * clause has been added as a safeguard if other types of<a name="line.191"></a>
<FONT color="green">192</FONT>                     * normalizations are ever implemented, and the corresponding<a name="line.192"></a>
<FONT color="green">193</FONT>                     * test is forgotten in the present switch.<a name="line.193"></a>
<FONT color="green">194</FONT>                     */<a name="line.194"></a>
<FONT color="green">195</FONT>                    throw new MathIllegalStateException();<a name="line.195"></a>
<FONT color="green">196</FONT>            }<a name="line.196"></a>
<FONT color="green">197</FONT>        }<a name="line.197"></a>
<FONT color="green">198</FONT>    <a name="line.198"></a>
<FONT color="green">199</FONT>        /**<a name="line.199"></a>
<FONT color="green">200</FONT>         * Computes the standard transform of the specified complex data. The<a name="line.200"></a>
<FONT color="green">201</FONT>         * computation is done in place. The input data is laid out as follows<a name="line.201"></a>
<FONT color="green">202</FONT>         * &lt;ul&gt;<a name="line.202"></a>
<FONT color="green">203</FONT>         *   &lt;li&gt;{@code dataRI[0][i]} is the real part of the {@code i}-th data point,&lt;/li&gt;<a name="line.203"></a>
<FONT color="green">204</FONT>         *   &lt;li&gt;{@code dataRI[1][i]} is the imaginary part of the {@code i}-th data point.&lt;/li&gt;<a name="line.204"></a>
<FONT color="green">205</FONT>         * &lt;/ul&gt;<a name="line.205"></a>
<FONT color="green">206</FONT>         *<a name="line.206"></a>
<FONT color="green">207</FONT>         * @param dataRI the two dimensional array of real and imaginary parts of the data<a name="line.207"></a>
<FONT color="green">208</FONT>         * @param normalization the normalization to be applied to the transformed data<a name="line.208"></a>
<FONT color="green">209</FONT>         * @param type the type of transform (forward, inverse) to be performed<a name="line.209"></a>
<FONT color="green">210</FONT>         * @throws DimensionMismatchException if the number of rows of the specified<a name="line.210"></a>
<FONT color="green">211</FONT>         *   array is not two, or the array is not rectangular<a name="line.211"></a>
<FONT color="green">212</FONT>         * @throws MathIllegalArgumentException if the number of data points is not<a name="line.212"></a>
<FONT color="green">213</FONT>         *   a power of two<a name="line.213"></a>
<FONT color="green">214</FONT>         */<a name="line.214"></a>
<FONT color="green">215</FONT>        public static void transformInPlace(final double[][] dataRI,<a name="line.215"></a>
<FONT color="green">216</FONT>            final DftNormalization normalization, final TransformType type) {<a name="line.216"></a>
<FONT color="green">217</FONT>    <a name="line.217"></a>
<FONT color="green">218</FONT>            if (dataRI.length != 2) {<a name="line.218"></a>
<FONT color="green">219</FONT>                throw new DimensionMismatchException(dataRI.length, 2);<a name="line.219"></a>
<FONT color="green">220</FONT>            }<a name="line.220"></a>
<FONT color="green">221</FONT>            final double[] dataR = dataRI[0];<a name="line.221"></a>
<FONT color="green">222</FONT>            final double[] dataI = dataRI[1];<a name="line.222"></a>
<FONT color="green">223</FONT>            if (dataR.length != dataI.length) {<a name="line.223"></a>
<FONT color="green">224</FONT>                throw new DimensionMismatchException(dataI.length, dataR.length);<a name="line.224"></a>
<FONT color="green">225</FONT>            }<a name="line.225"></a>
<FONT color="green">226</FONT>    <a name="line.226"></a>
<FONT color="green">227</FONT>            final int n = dataR.length;<a name="line.227"></a>
<FONT color="green">228</FONT>            if (!ArithmeticUtils.isPowerOfTwo(n)) {<a name="line.228"></a>
<FONT color="green">229</FONT>                throw new MathIllegalArgumentException(<a name="line.229"></a>
<FONT color="green">230</FONT>                    LocalizedFormats.NOT_POWER_OF_TWO_CONSIDER_PADDING,<a name="line.230"></a>
<FONT color="green">231</FONT>                    Integer.valueOf(n));<a name="line.231"></a>
<FONT color="green">232</FONT>            }<a name="line.232"></a>
<FONT color="green">233</FONT>    <a name="line.233"></a>
<FONT color="green">234</FONT>            if (n == 1) {<a name="line.234"></a>
<FONT color="green">235</FONT>                return;<a name="line.235"></a>
<FONT color="green">236</FONT>            } else if (n == 2) {<a name="line.236"></a>
<FONT color="green">237</FONT>                final double srcR0 = dataR[0];<a name="line.237"></a>
<FONT color="green">238</FONT>                final double srcI0 = dataI[0];<a name="line.238"></a>
<FONT color="green">239</FONT>                final double srcR1 = dataR[1];<a name="line.239"></a>
<FONT color="green">240</FONT>                final double srcI1 = dataI[1];<a name="line.240"></a>
<FONT color="green">241</FONT>    <a name="line.241"></a>
<FONT color="green">242</FONT>                // X_0 = x_0 + x_1<a name="line.242"></a>
<FONT color="green">243</FONT>                dataR[0] = srcR0 + srcR1;<a name="line.243"></a>
<FONT color="green">244</FONT>                dataI[0] = srcI0 + srcI1;<a name="line.244"></a>
<FONT color="green">245</FONT>                // X_1 = x_0 - x_1<a name="line.245"></a>
<FONT color="green">246</FONT>                dataR[1] = srcR0 - srcR1;<a name="line.246"></a>
<FONT color="green">247</FONT>                dataI[1] = srcI0 - srcI1;<a name="line.247"></a>
<FONT color="green">248</FONT>    <a name="line.248"></a>
<FONT color="green">249</FONT>                normalizeTransformedData(dataRI, normalization, type);<a name="line.249"></a>
<FONT color="green">250</FONT>                return;<a name="line.250"></a>
<FONT color="green">251</FONT>            }<a name="line.251"></a>
<FONT color="green">252</FONT>    <a name="line.252"></a>
<FONT color="green">253</FONT>            bitReversalShuffle2(dataR, dataI);<a name="line.253"></a>
<FONT color="green">254</FONT>    <a name="line.254"></a>
<FONT color="green">255</FONT>            // Do 4-term DFT.<a name="line.255"></a>
<FONT color="green">256</FONT>            if (type == TransformType.INVERSE) {<a name="line.256"></a>
<FONT color="green">257</FONT>                for (int i0 = 0; i0 &lt; n; i0 += 4) {<a name="line.257"></a>
<FONT color="green">258</FONT>                    final int i1 = i0 + 1;<a name="line.258"></a>
<FONT color="green">259</FONT>                    final int i2 = i0 + 2;<a name="line.259"></a>
<FONT color="green">260</FONT>                    final int i3 = i0 + 3;<a name="line.260"></a>
<FONT color="green">261</FONT>    <a name="line.261"></a>
<FONT color="green">262</FONT>                    final double srcR0 = dataR[i0];<a name="line.262"></a>
<FONT color="green">263</FONT>                    final double srcI0 = dataI[i0];<a name="line.263"></a>
<FONT color="green">264</FONT>                    final double srcR1 = dataR[i2];<a name="line.264"></a>
<FONT color="green">265</FONT>                    final double srcI1 = dataI[i2];<a name="line.265"></a>
<FONT color="green">266</FONT>                    final double srcR2 = dataR[i1];<a name="line.266"></a>
<FONT color="green">267</FONT>                    final double srcI2 = dataI[i1];<a name="line.267"></a>
<FONT color="green">268</FONT>                    final double srcR3 = dataR[i3];<a name="line.268"></a>
<FONT color="green">269</FONT>                    final double srcI3 = dataI[i3];<a name="line.269"></a>
<FONT color="green">270</FONT>    <a name="line.270"></a>
<FONT color="green">271</FONT>                    // 4-term DFT<a name="line.271"></a>
<FONT color="green">272</FONT>                    // X_0 = x_0 + x_1 + x_2 + x_3<a name="line.272"></a>
<FONT color="green">273</FONT>                    dataR[i0] = srcR0 + srcR1 + srcR2 + srcR3;<a name="line.273"></a>
<FONT color="green">274</FONT>                    dataI[i0] = srcI0 + srcI1 + srcI2 + srcI3;<a name="line.274"></a>
<FONT color="green">275</FONT>                    // X_1 = x_0 - x_2 + j * (x_3 - x_1)<a name="line.275"></a>
<FONT color="green">276</FONT>                    dataR[i1] = srcR0 - srcR2 + (srcI3 - srcI1);<a name="line.276"></a>
<FONT color="green">277</FONT>                    dataI[i1] = srcI0 - srcI2 + (srcR1 - srcR3);<a name="line.277"></a>
<FONT color="green">278</FONT>                    // X_2 = x_0 - x_1 + x_2 - x_3<a name="line.278"></a>
<FONT color="green">279</FONT>                    dataR[i2] = srcR0 - srcR1 + srcR2 - srcR3;<a name="line.279"></a>
<FONT color="green">280</FONT>                    dataI[i2] = srcI0 - srcI1 + srcI2 - srcI3;<a name="line.280"></a>
<FONT color="green">281</FONT>                    // X_3 = x_0 - x_2 + j * (x_1 - x_3)<a name="line.281"></a>
<FONT color="green">282</FONT>                    dataR[i3] = srcR0 - srcR2 + (srcI1 - srcI3);<a name="line.282"></a>
<FONT color="green">283</FONT>                    dataI[i3] = srcI0 - srcI2 + (srcR3 - srcR1);<a name="line.283"></a>
<FONT color="green">284</FONT>                }<a name="line.284"></a>
<FONT color="green">285</FONT>            } else {<a name="line.285"></a>
<FONT color="green">286</FONT>                for (int i0 = 0; i0 &lt; n; i0 += 4) {<a name="line.286"></a>
<FONT color="green">287</FONT>                    final int i1 = i0 + 1;<a name="line.287"></a>
<FONT color="green">288</FONT>                    final int i2 = i0 + 2;<a name="line.288"></a>
<FONT color="green">289</FONT>                    final int i3 = i0 + 3;<a name="line.289"></a>
<FONT color="green">290</FONT>    <a name="line.290"></a>
<FONT color="green">291</FONT>                    final double srcR0 = dataR[i0];<a name="line.291"></a>
<FONT color="green">292</FONT>                    final double srcI0 = dataI[i0];<a name="line.292"></a>
<FONT color="green">293</FONT>                    final double srcR1 = dataR[i2];<a name="line.293"></a>
<FONT color="green">294</FONT>                    final double srcI1 = dataI[i2];<a name="line.294"></a>
<FONT color="green">295</FONT>                    final double srcR2 = dataR[i1];<a name="line.295"></a>
<FONT color="green">296</FONT>                    final double srcI2 = dataI[i1];<a name="line.296"></a>
<FONT color="green">297</FONT>                    final double srcR3 = dataR[i3];<a name="line.297"></a>
<FONT color="green">298</FONT>                    final double srcI3 = dataI[i3];<a name="line.298"></a>
<FONT color="green">299</FONT>    <a name="line.299"></a>
<FONT color="green">300</FONT>                    // 4-term DFT<a name="line.300"></a>
<FONT color="green">301</FONT>                    // X_0 = x_0 + x_1 + x_2 + x_3<a name="line.301"></a>
<FONT color="green">302</FONT>                    dataR[i0] = srcR0 + srcR1 + srcR2 + srcR3;<a name="line.302"></a>
<FONT color="green">303</FONT>                    dataI[i0] = srcI0 + srcI1 + srcI2 + srcI3;<a name="line.303"></a>
<FONT color="green">304</FONT>                    // X_1 = x_0 - x_2 + j * (x_3 - x_1)<a name="line.304"></a>
<FONT color="green">305</FONT>                    dataR[i1] = srcR0 - srcR2 + (srcI1 - srcI3);<a name="line.305"></a>
<FONT color="green">306</FONT>                    dataI[i1] = srcI0 - srcI2 + (srcR3 - srcR1);<a name="line.306"></a>
<FONT color="green">307</FONT>                    // X_2 = x_0 - x_1 + x_2 - x_3<a name="line.307"></a>
<FONT color="green">308</FONT>                    dataR[i2] = srcR0 - srcR1 + srcR2 - srcR3;<a name="line.308"></a>
<FONT color="green">309</FONT>                    dataI[i2] = srcI0 - srcI1 + srcI2 - srcI3;<a name="line.309"></a>
<FONT color="green">310</FONT>                    // X_3 = x_0 - x_2 + j * (x_1 - x_3)<a name="line.310"></a>
<FONT color="green">311</FONT>                    dataR[i3] = srcR0 - srcR2 + (srcI3 - srcI1);<a name="line.311"></a>
<FONT color="green">312</FONT>                    dataI[i3] = srcI0 - srcI2 + (srcR1 - srcR3);<a name="line.312"></a>
<FONT color="green">313</FONT>                }<a name="line.313"></a>
<FONT color="green">314</FONT>            }<a name="line.314"></a>
<FONT color="green">315</FONT>    <a name="line.315"></a>
<FONT color="green">316</FONT>            int lastN0 = 4;<a name="line.316"></a>
<FONT color="green">317</FONT>            int lastLogN0 = 2;<a name="line.317"></a>
<FONT color="green">318</FONT>            while (lastN0 &lt; n) {<a name="line.318"></a>
<FONT color="green">319</FONT>                int n0 = lastN0 &lt;&lt; 1;<a name="line.319"></a>
<FONT color="green">320</FONT>                int logN0 = lastLogN0 + 1;<a name="line.320"></a>
<FONT color="green">321</FONT>                double wSubN0R = W_SUB_N_R[logN0];<a name="line.321"></a>
<FONT color="green">322</FONT>                double wSubN0I = W_SUB_N_I[logN0];<a name="line.322"></a>
<FONT color="green">323</FONT>                if (type == TransformType.INVERSE) {<a name="line.323"></a>
<FONT color="green">324</FONT>                    wSubN0I = -wSubN0I;<a name="line.324"></a>
<FONT color="green">325</FONT>                }<a name="line.325"></a>
<FONT color="green">326</FONT>    <a name="line.326"></a>
<FONT color="green">327</FONT>                // Combine even/odd transforms of size lastN0 into a transform of size N0 (lastN0 * 2).<a name="line.327"></a>
<FONT color="green">328</FONT>                for (int destEvenStartIndex = 0; destEvenStartIndex &lt; n; destEvenStartIndex += n0) {<a name="line.328"></a>
<FONT color="green">329</FONT>                    int destOddStartIndex = destEvenStartIndex + lastN0;<a name="line.329"></a>
<FONT color="green">330</FONT>    <a name="line.330"></a>
<FONT color="green">331</FONT>                    double wSubN0ToRR = 1;<a name="line.331"></a>
<FONT color="green">332</FONT>                    double wSubN0ToRI = 0;<a name="line.332"></a>
<FONT color="green">333</FONT>    <a name="line.333"></a>
<FONT color="green">334</FONT>                    for (int r = 0; r &lt; lastN0; r++) {<a name="line.334"></a>
<FONT color="green">335</FONT>                        double grR = dataR[destEvenStartIndex + r];<a name="line.335"></a>
<FONT color="green">336</FONT>                        double grI = dataI[destEvenStartIndex + r];<a name="line.336"></a>
<FONT color="green">337</FONT>                        double hrR = dataR[destOddStartIndex + r];<a name="line.337"></a>
<FONT color="green">338</FONT>                        double hrI = dataI[destOddStartIndex + r];<a name="line.338"></a>
<FONT color="green">339</FONT>    <a name="line.339"></a>
<FONT color="green">340</FONT>                        // dest[destEvenStartIndex + r] = Gr + WsubN0ToR * Hr<a name="line.340"></a>
<FONT color="green">341</FONT>                        dataR[destEvenStartIndex + r] = grR + wSubN0ToRR * hrR - wSubN0ToRI * hrI;<a name="line.341"></a>
<FONT color="green">342</FONT>                        dataI[destEvenStartIndex + r] = grI + wSubN0ToRR * hrI + wSubN0ToRI * hrR;<a name="line.342"></a>
<FONT color="green">343</FONT>                        // dest[destOddStartIndex + r] = Gr - WsubN0ToR * Hr<a name="line.343"></a>
<FONT color="green">344</FONT>                        dataR[destOddStartIndex + r] = grR - (wSubN0ToRR * hrR - wSubN0ToRI * hrI);<a name="line.344"></a>
<FONT color="green">345</FONT>                        dataI[destOddStartIndex + r] = grI - (wSubN0ToRR * hrI + wSubN0ToRI * hrR);<a name="line.345"></a>
<FONT color="green">346</FONT>    <a name="line.346"></a>
<FONT color="green">347</FONT>                        // WsubN0ToR *= WsubN0R<a name="line.347"></a>
<FONT color="green">348</FONT>                        double nextWsubN0ToRR = wSubN0ToRR * wSubN0R - wSubN0ToRI * wSubN0I;<a name="line.348"></a>
<FONT color="green">349</FONT>                        double nextWsubN0ToRI = wSubN0ToRR * wSubN0I + wSubN0ToRI * wSubN0R;<a name="line.349"></a>
<FONT color="green">350</FONT>                        wSubN0ToRR = nextWsubN0ToRR;<a name="line.350"></a>
<FONT color="green">351</FONT>                        wSubN0ToRI = nextWsubN0ToRI;<a name="line.351"></a>
<FONT color="green">352</FONT>                    }<a name="line.352"></a>
<FONT color="green">353</FONT>                }<a name="line.353"></a>
<FONT color="green">354</FONT>    <a name="line.354"></a>
<FONT color="green">355</FONT>                lastN0 = n0;<a name="line.355"></a>
<FONT color="green">356</FONT>                lastLogN0 = logN0;<a name="line.356"></a>
<FONT color="green">357</FONT>            }<a name="line.357"></a>
<FONT color="green">358</FONT>    <a name="line.358"></a>
<FONT color="green">359</FONT>            normalizeTransformedData(dataRI, normalization, type);<a name="line.359"></a>
<FONT color="green">360</FONT>        }<a name="line.360"></a>
<FONT color="green">361</FONT>    <a name="line.361"></a>
<FONT color="green">362</FONT>        /**<a name="line.362"></a>
<FONT color="green">363</FONT>         * Returns the (forward, inverse) transform of the specified real data set.<a name="line.363"></a>
<FONT color="green">364</FONT>         *<a name="line.364"></a>
<FONT color="green">365</FONT>         * @param f the real data array to be transformed<a name="line.365"></a>
<FONT color="green">366</FONT>         * @param type the type of transform (forward, inverse) to be performed<a name="line.366"></a>
<FONT color="green">367</FONT>         * @return the complex transformed array<a name="line.367"></a>
<FONT color="green">368</FONT>         * @throws MathIllegalArgumentException if the length of the data array is not a power of two<a name="line.368"></a>
<FONT color="green">369</FONT>         */<a name="line.369"></a>
<FONT color="green">370</FONT>        public Complex[] transform(final double[] f, final TransformType type) {<a name="line.370"></a>
<FONT color="green">371</FONT>            final double[][] dataRI = new double[][] {<a name="line.371"></a>
<FONT color="green">372</FONT>                MathArrays.copyOf(f, f.length), new double[f.length]<a name="line.372"></a>
<FONT color="green">373</FONT>            };<a name="line.373"></a>
<FONT color="green">374</FONT>    <a name="line.374"></a>
<FONT color="green">375</FONT>            transformInPlace(dataRI, normalization, type);<a name="line.375"></a>
<FONT color="green">376</FONT>    <a name="line.376"></a>
<FONT color="green">377</FONT>            return TransformUtils.createComplexArray(dataRI);<a name="line.377"></a>
<FONT color="green">378</FONT>        }<a name="line.378"></a>
<FONT color="green">379</FONT>    <a name="line.379"></a>
<FONT color="green">380</FONT>        /**<a name="line.380"></a>
<FONT color="green">381</FONT>         * Returns the (forward, inverse) transform of the specified real function,<a name="line.381"></a>
<FONT color="green">382</FONT>         * sampled on the specified interval.<a name="line.382"></a>
<FONT color="green">383</FONT>         *<a name="line.383"></a>
<FONT color="green">384</FONT>         * @param f the function to be sampled and transformed<a name="line.384"></a>
<FONT color="green">385</FONT>         * @param min the (inclusive) lower bound for the interval<a name="line.385"></a>
<FONT color="green">386</FONT>         * @param max the (exclusive) upper bound for the interval<a name="line.386"></a>
<FONT color="green">387</FONT>         * @param n the number of sample points<a name="line.387"></a>
<FONT color="green">388</FONT>         * @param type the type of transform (forward, inverse) to be performed<a name="line.388"></a>
<FONT color="green">389</FONT>         * @return the complex transformed array<a name="line.389"></a>
<FONT color="green">390</FONT>         * @throws org.apache.commons.math3.exception.NumberIsTooLargeException<a name="line.390"></a>
<FONT color="green">391</FONT>         *   if the lower bound is greater than, or equal to the upper bound<a name="line.391"></a>
<FONT color="green">392</FONT>         * @throws org.apache.commons.math3.exception.NotStrictlyPositiveException<a name="line.392"></a>
<FONT color="green">393</FONT>         *   if the number of sample points {@code n} is negative<a name="line.393"></a>
<FONT color="green">394</FONT>         * @throws MathIllegalArgumentException if the number of sample points<a name="line.394"></a>
<FONT color="green">395</FONT>         *   {@code n} is not a power of two<a name="line.395"></a>
<FONT color="green">396</FONT>         */<a name="line.396"></a>
<FONT color="green">397</FONT>        public Complex[] transform(final UnivariateFunction f,<a name="line.397"></a>
<FONT color="green">398</FONT>                                   final double min, final double max, final int n,<a name="line.398"></a>
<FONT color="green">399</FONT>                                   final TransformType type) {<a name="line.399"></a>
<FONT color="green">400</FONT>    <a name="line.400"></a>
<FONT color="green">401</FONT>            final double[] data = FunctionUtils.sample(f, min, max, n);<a name="line.401"></a>
<FONT color="green">402</FONT>            return transform(data, type);<a name="line.402"></a>
<FONT color="green">403</FONT>        }<a name="line.403"></a>
<FONT color="green">404</FONT>    <a name="line.404"></a>
<FONT color="green">405</FONT>        /**<a name="line.405"></a>
<FONT color="green">406</FONT>         * Returns the (forward, inverse) transform of the specified complex data set.<a name="line.406"></a>
<FONT color="green">407</FONT>         *<a name="line.407"></a>
<FONT color="green">408</FONT>         * @param f the complex data array to be transformed<a name="line.408"></a>
<FONT color="green">409</FONT>         * @param type the type of transform (forward, inverse) to be performed<a name="line.409"></a>
<FONT color="green">410</FONT>         * @return the complex transformed array<a name="line.410"></a>
<FONT color="green">411</FONT>         * @throws MathIllegalArgumentException if the length of the data array is not a power of two<a name="line.411"></a>
<FONT color="green">412</FONT>         */<a name="line.412"></a>
<FONT color="green">413</FONT>        public Complex[] transform(final Complex[] f, final TransformType type) {<a name="line.413"></a>
<FONT color="green">414</FONT>            final double[][] dataRI = TransformUtils.createRealImaginaryArray(f);<a name="line.414"></a>
<FONT color="green">415</FONT>    <a name="line.415"></a>
<FONT color="green">416</FONT>            transformInPlace(dataRI, normalization, type);<a name="line.416"></a>
<FONT color="green">417</FONT>    <a name="line.417"></a>
<FONT color="green">418</FONT>            return TransformUtils.createComplexArray(dataRI);<a name="line.418"></a>
<FONT color="green">419</FONT>        }<a name="line.419"></a>
<FONT color="green">420</FONT>    <a name="line.420"></a>
<FONT color="green">421</FONT>        /**<a name="line.421"></a>
<FONT color="green">422</FONT>         * Performs a multi-dimensional Fourier transform on a given array. Use<a name="line.422"></a>
<FONT color="green">423</FONT>         * {@link #transform(Complex[], TransformType)} in a row-column<a name="line.423"></a>
<FONT color="green">424</FONT>         * implementation in any number of dimensions with<a name="line.424"></a>
<FONT color="green">425</FONT>         * O(N&amp;times;log(N)) complexity with<a name="line.425"></a>
<FONT color="green">426</FONT>         * N = n&lt;sub&gt;1&lt;/sub&gt; &amp;times; n&lt;sub&gt;2&lt;/sub&gt; &amp;times;n&lt;sub&gt;3&lt;/sub&gt; &amp;times; ...<a name="line.426"></a>
<FONT color="green">427</FONT>         * &amp;times; n&lt;sub&gt;d&lt;/sub&gt;, where n&lt;sub&gt;k&lt;/sub&gt; is the number of elements in<a name="line.427"></a>
<FONT color="green">428</FONT>         * dimension k, and d is the total number of dimensions.<a name="line.428"></a>
<FONT color="green">429</FONT>         *<a name="line.429"></a>
<FONT color="green">430</FONT>         * @param mdca Multi-Dimensional Complex Array, i.e. {@code Complex[][][][]}<a name="line.430"></a>
<FONT color="green">431</FONT>         * @param type the type of transform (forward, inverse) to be performed<a name="line.431"></a>
<FONT color="green">432</FONT>         * @return transform of {@code mdca} as a Multi-Dimensional Complex Array, i.e. {@code Complex[][][][]}<a name="line.432"></a>
<FONT color="green">433</FONT>         * @throws IllegalArgumentException if any dimension is not a power of two<a name="line.433"></a>
<FONT color="green">434</FONT>         * @deprecated see MATH-736<a name="line.434"></a>
<FONT color="green">435</FONT>         */<a name="line.435"></a>
<FONT color="green">436</FONT>        @Deprecated<a name="line.436"></a>
<FONT color="green">437</FONT>        public Object mdfft(Object mdca, TransformType type) {<a name="line.437"></a>
<FONT color="green">438</FONT>            MultiDimensionalComplexMatrix mdcm = (MultiDimensionalComplexMatrix)<a name="line.438"></a>
<FONT color="green">439</FONT>                    new MultiDimensionalComplexMatrix(mdca).clone();<a name="line.439"></a>
<FONT color="green">440</FONT>            int[] dimensionSize = mdcm.getDimensionSizes();<a name="line.440"></a>
<FONT color="green">441</FONT>            //cycle through each dimension<a name="line.441"></a>
<FONT color="green">442</FONT>            for (int i = 0; i &lt; dimensionSize.length; i++) {<a name="line.442"></a>
<FONT color="green">443</FONT>                mdfft(mdcm, type, i, new int[0]);<a name="line.443"></a>
<FONT color="green">444</FONT>            }<a name="line.444"></a>
<FONT color="green">445</FONT>            return mdcm.getArray();<a name="line.445"></a>
<FONT color="green">446</FONT>        }<a name="line.446"></a>
<FONT color="green">447</FONT>    <a name="line.447"></a>
<FONT color="green">448</FONT>        /**<a name="line.448"></a>
<FONT color="green">449</FONT>         * Performs one dimension of a multi-dimensional Fourier transform.<a name="line.449"></a>
<FONT color="green">450</FONT>         *<a name="line.450"></a>
<FONT color="green">451</FONT>         * @param mdcm input matrix<a name="line.451"></a>
<FONT color="green">452</FONT>         * @param type the type of transform (forward, inverse) to be performed<a name="line.452"></a>
<FONT color="green">453</FONT>         * @param d index of the dimension to process<a name="line.453"></a>
<FONT color="green">454</FONT>         * @param subVector recursion subvector<a name="line.454"></a>
<FONT color="green">455</FONT>         * @throws IllegalArgumentException if any dimension is not a power of two<a name="line.455"></a>
<FONT color="green">456</FONT>         * @deprecated see MATH-736<a name="line.456"></a>
<FONT color="green">457</FONT>         */<a name="line.457"></a>
<FONT color="green">458</FONT>        @Deprecated<a name="line.458"></a>
<FONT color="green">459</FONT>        private void mdfft(MultiDimensionalComplexMatrix mdcm,<a name="line.459"></a>
<FONT color="green">460</FONT>                TransformType type, int d, int[] subVector) {<a name="line.460"></a>
<FONT color="green">461</FONT>    <a name="line.461"></a>
<FONT color="green">462</FONT>            int[] dimensionSize = mdcm.getDimensionSizes();<a name="line.462"></a>
<FONT color="green">463</FONT>            //if done<a name="line.463"></a>
<FONT color="green">464</FONT>            if (subVector.length == dimensionSize.length) {<a name="line.464"></a>
<FONT color="green">465</FONT>                Complex[] temp = new Complex[dimensionSize[d]];<a name="line.465"></a>
<FONT color="green">466</FONT>                for (int i = 0; i &lt; dimensionSize[d]; i++) {<a name="line.466"></a>
<FONT color="green">467</FONT>                    //fft along dimension d<a name="line.467"></a>
<FONT color="green">468</FONT>                    subVector[d] = i;<a name="line.468"></a>
<FONT color="green">469</FONT>                    temp[i] = mdcm.get(subVector);<a name="line.469"></a>
<FONT color="green">470</FONT>                }<a name="line.470"></a>
<FONT color="green">471</FONT>    <a name="line.471"></a>
<FONT color="green">472</FONT>                temp = transform(temp, type);<a name="line.472"></a>
<FONT color="green">473</FONT>    <a name="line.473"></a>
<FONT color="green">474</FONT>                for (int i = 0; i &lt; dimensionSize[d]; i++) {<a name="line.474"></a>
<FONT color="green">475</FONT>                    subVector[d] = i;<a name="line.475"></a>
<FONT color="green">476</FONT>                    mdcm.set(temp[i], subVector);<a name="line.476"></a>
<FONT color="green">477</FONT>                }<a name="line.477"></a>
<FONT color="green">478</FONT>            } else {<a name="line.478"></a>
<FONT color="green">479</FONT>                int[] vector = new int[subVector.length + 1];<a name="line.479"></a>
<FONT color="green">480</FONT>                System.arraycopy(subVector, 0, vector, 0, subVector.length);<a name="line.480"></a>
<FONT color="green">481</FONT>                if (subVector.length == d) {<a name="line.481"></a>
<FONT color="green">482</FONT>                    //value is not important once the recursion is done.<a name="line.482"></a>
<FONT color="green">483</FONT>                    //then an fft will be applied along the dimension d.<a name="line.483"></a>
<FONT color="green">484</FONT>                    vector[d] = 0;<a name="line.484"></a>
<FONT color="green">485</FONT>                    mdfft(mdcm, type, d, vector);<a name="line.485"></a>
<FONT color="green">486</FONT>                } else {<a name="line.486"></a>
<FONT color="green">487</FONT>                    for (int i = 0; i &lt; dimensionSize[subVector.length]; i++) {<a name="line.487"></a>
<FONT color="green">488</FONT>                        vector[subVector.length] = i;<a name="line.488"></a>
<FONT color="green">489</FONT>                        //further split along the next dimension<a name="line.489"></a>
<FONT color="green">490</FONT>                        mdfft(mdcm, type, d, vector);<a name="line.490"></a>
<FONT color="green">491</FONT>                    }<a name="line.491"></a>
<FONT color="green">492</FONT>                }<a name="line.492"></a>
<FONT color="green">493</FONT>            }<a name="line.493"></a>
<FONT color="green">494</FONT>        }<a name="line.494"></a>
<FONT color="green">495</FONT>    <a name="line.495"></a>
<FONT color="green">496</FONT>        /**<a name="line.496"></a>
<FONT color="green">497</FONT>         * Complex matrix implementation. Not designed for synchronized access may<a name="line.497"></a>
<FONT color="green">498</FONT>         * eventually be replaced by jsr-83 of the java community process<a name="line.498"></a>
<FONT color="green">499</FONT>         * http://jcp.org/en/jsr/detail?id=83<a name="line.499"></a>
<FONT color="green">500</FONT>         * may require additional exception throws for other basic requirements.<a name="line.500"></a>
<FONT color="green">501</FONT>         *<a name="line.501"></a>
<FONT color="green">502</FONT>         * @deprecated see MATH-736<a name="line.502"></a>
<FONT color="green">503</FONT>         */<a name="line.503"></a>
<FONT color="green">504</FONT>        @Deprecated<a name="line.504"></a>
<FONT color="green">505</FONT>        private static class MultiDimensionalComplexMatrix<a name="line.505"></a>
<FONT color="green">506</FONT>            implements Cloneable {<a name="line.506"></a>
<FONT color="green">507</FONT>    <a name="line.507"></a>
<FONT color="green">508</FONT>            /** Size in all dimensions. */<a name="line.508"></a>
<FONT color="green">509</FONT>            protected int[] dimensionSize;<a name="line.509"></a>
<FONT color="green">510</FONT>    <a name="line.510"></a>
<FONT color="green">511</FONT>            /** Storage array. */<a name="line.511"></a>
<FONT color="green">512</FONT>            protected Object multiDimensionalComplexArray;<a name="line.512"></a>
<FONT color="green">513</FONT>    <a name="line.513"></a>
<FONT color="green">514</FONT>            /**<a name="line.514"></a>
<FONT color="green">515</FONT>             * Simple constructor.<a name="line.515"></a>
<FONT color="green">516</FONT>             *<a name="line.516"></a>
<FONT color="green">517</FONT>             * @param multiDimensionalComplexArray array containing the matrix<a name="line.517"></a>
<FONT color="green">518</FONT>             * elements<a name="line.518"></a>
<FONT color="green">519</FONT>             */<a name="line.519"></a>
<FONT color="green">520</FONT>            public MultiDimensionalComplexMatrix(<a name="line.520"></a>
<FONT color="green">521</FONT>                    Object multiDimensionalComplexArray) {<a name="line.521"></a>
<FONT color="green">522</FONT>    <a name="line.522"></a>
<FONT color="green">523</FONT>                this.multiDimensionalComplexArray = multiDimensionalComplexArray;<a name="line.523"></a>
<FONT color="green">524</FONT>    <a name="line.524"></a>
<FONT color="green">525</FONT>                // count dimensions<a name="line.525"></a>
<FONT color="green">526</FONT>                int numOfDimensions = 0;<a name="line.526"></a>
<FONT color="green">527</FONT>                for (Object lastDimension = multiDimensionalComplexArray;<a name="line.527"></a>
<FONT color="green">528</FONT>                     lastDimension instanceof Object[];) {<a name="line.528"></a>
<FONT color="green">529</FONT>                    final Object[] array = (Object[]) lastDimension;<a name="line.529"></a>
<FONT color="green">530</FONT>                    numOfDimensions++;<a name="line.530"></a>
<FONT color="green">531</FONT>                    lastDimension = array[0];<a name="line.531"></a>
<FONT color="green">532</FONT>                }<a name="line.532"></a>
<FONT color="green">533</FONT>    <a name="line.533"></a>
<FONT color="green">534</FONT>                // allocate array with exact count<a name="line.534"></a>
<FONT color="green">535</FONT>                dimensionSize = new int[numOfDimensions];<a name="line.535"></a>
<FONT color="green">536</FONT>    <a name="line.536"></a>
<FONT color="green">537</FONT>                // fill array<a name="line.537"></a>
<FONT color="green">538</FONT>                numOfDimensions = 0;<a name="line.538"></a>
<FONT color="green">539</FONT>                for (Object lastDimension = multiDimensionalComplexArray;<a name="line.539"></a>
<FONT color="green">540</FONT>                     lastDimension instanceof Object[];) {<a name="line.540"></a>
<FONT color="green">541</FONT>                    final Object[] array = (Object[]) lastDimension;<a name="line.541"></a>
<FONT color="green">542</FONT>                    dimensionSize[numOfDimensions++] = array.length;<a name="line.542"></a>
<FONT color="green">543</FONT>                    lastDimension = array[0];<a name="line.543"></a>
<FONT color="green">544</FONT>                }<a name="line.544"></a>
<FONT color="green">545</FONT>    <a name="line.545"></a>
<FONT color="green">546</FONT>            }<a name="line.546"></a>
<FONT color="green">547</FONT>    <a name="line.547"></a>
<FONT color="green">548</FONT>            /**<a name="line.548"></a>
<FONT color="green">549</FONT>             * Get a matrix element.<a name="line.549"></a>
<FONT color="green">550</FONT>             *<a name="line.550"></a>
<FONT color="green">551</FONT>             * @param vector indices of the element<a name="line.551"></a>
<FONT color="green">552</FONT>             * @return matrix element<a name="line.552"></a>
<FONT color="green">553</FONT>             * @exception DimensionMismatchException if dimensions do not match<a name="line.553"></a>
<FONT color="green">554</FONT>             */<a name="line.554"></a>
<FONT color="green">555</FONT>            public Complex get(int... vector)<a name="line.555"></a>
<FONT color="green">556</FONT>                    throws DimensionMismatchException {<a name="line.556"></a>
<FONT color="green">557</FONT>    <a name="line.557"></a>
<FONT color="green">558</FONT>                if (vector == null) {<a name="line.558"></a>
<FONT color="green">559</FONT>                    if (dimensionSize.length &gt; 0) {<a name="line.559"></a>
<FONT color="green">560</FONT>                        throw new DimensionMismatchException(<a name="line.560"></a>
<FONT color="green">561</FONT>                                0,<a name="line.561"></a>
<FONT color="green">562</FONT>                                dimensionSize.length);<a name="line.562"></a>
<FONT color="green">563</FONT>                    }<a name="line.563"></a>
<FONT color="green">564</FONT>                    return null;<a name="line.564"></a>
<FONT color="green">565</FONT>                }<a name="line.565"></a>
<FONT color="green">566</FONT>                if (vector.length != dimensionSize.length) {<a name="line.566"></a>
<FONT color="green">567</FONT>                    throw new DimensionMismatchException(<a name="line.567"></a>
<FONT color="green">568</FONT>                            vector.length,<a name="line.568"></a>
<FONT color="green">569</FONT>                            dimensionSize.length);<a name="line.569"></a>
<FONT color="green">570</FONT>                }<a name="line.570"></a>
<FONT color="green">571</FONT>    <a name="line.571"></a>
<FONT color="green">572</FONT>                Object lastDimension = multiDimensionalComplexArray;<a name="line.572"></a>
<FONT color="green">573</FONT>    <a name="line.573"></a>
<FONT color="green">574</FONT>                for (int i = 0; i &lt; dimensionSize.length; i++) {<a name="line.574"></a>
<FONT color="green">575</FONT>                    lastDimension = ((Object[]) lastDimension)[vector[i]];<a name="line.575"></a>
<FONT color="green">576</FONT>                }<a name="line.576"></a>
<FONT color="green">577</FONT>                return (Complex) lastDimension;<a name="line.577"></a>
<FONT color="green">578</FONT>            }<a name="line.578"></a>
<FONT color="green">579</FONT>    <a name="line.579"></a>
<FONT color="green">580</FONT>            /**<a name="line.580"></a>
<FONT color="green">581</FONT>             * Set a matrix element.<a name="line.581"></a>
<FONT color="green">582</FONT>             *<a name="line.582"></a>
<FONT color="green">583</FONT>             * @param magnitude magnitude of the element<a name="line.583"></a>
<FONT color="green">584</FONT>             * @param vector indices of the element<a name="line.584"></a>
<FONT color="green">585</FONT>             * @return the previous value<a name="line.585"></a>
<FONT color="green">586</FONT>             * @exception DimensionMismatchException if dimensions do not match<a name="line.586"></a>
<FONT color="green">587</FONT>             */<a name="line.587"></a>
<FONT color="green">588</FONT>            public Complex set(Complex magnitude, int... vector)<a name="line.588"></a>
<FONT color="green">589</FONT>                    throws DimensionMismatchException {<a name="line.589"></a>
<FONT color="green">590</FONT>    <a name="line.590"></a>
<FONT color="green">591</FONT>                if (vector == null) {<a name="line.591"></a>
<FONT color="green">592</FONT>                    if (dimensionSize.length &gt; 0) {<a name="line.592"></a>
<FONT color="green">593</FONT>                        throw new DimensionMismatchException(<a name="line.593"></a>
<FONT color="green">594</FONT>                                0,<a name="line.594"></a>
<FONT color="green">595</FONT>                                dimensionSize.length);<a name="line.595"></a>
<FONT color="green">596</FONT>                    }<a name="line.596"></a>
<FONT color="green">597</FONT>                    return null;<a name="line.597"></a>
<FONT color="green">598</FONT>                }<a name="line.598"></a>
<FONT color="green">599</FONT>                if (vector.length != dimensionSize.length) {<a name="line.599"></a>
<FONT color="green">600</FONT>                    throw new DimensionMismatchException(<a name="line.600"></a>
<FONT color="green">601</FONT>                            vector.length,<a name="line.601"></a>
<FONT color="green">602</FONT>                            dimensionSize.length);<a name="line.602"></a>
<FONT color="green">603</FONT>                }<a name="line.603"></a>
<FONT color="green">604</FONT>    <a name="line.604"></a>
<FONT color="green">605</FONT>                Object[] lastDimension = (Object[]) multiDimensionalComplexArray;<a name="line.605"></a>
<FONT color="green">606</FONT>                for (int i = 0; i &lt; dimensionSize.length - 1; i++) {<a name="line.606"></a>
<FONT color="green">607</FONT>                    lastDimension = (Object[]) lastDimension[vector[i]];<a name="line.607"></a>
<FONT color="green">608</FONT>                }<a name="line.608"></a>
<FONT color="green">609</FONT>    <a name="line.609"></a>
<FONT color="green">610</FONT>                Complex lastValue = (Complex) lastDimension[vector[dimensionSize.length - 1]];<a name="line.610"></a>
<FONT color="green">611</FONT>                lastDimension[vector[dimensionSize.length - 1]] = magnitude;<a name="line.611"></a>
<FONT color="green">612</FONT>    <a name="line.612"></a>
<FONT color="green">613</FONT>                return lastValue;<a name="line.613"></a>
<FONT color="green">614</FONT>            }<a name="line.614"></a>
<FONT color="green">615</FONT>    <a name="line.615"></a>
<FONT color="green">616</FONT>            /**<a name="line.616"></a>
<FONT color="green">617</FONT>             * Get the size in all dimensions.<a name="line.617"></a>
<FONT color="green">618</FONT>             *<a name="line.618"></a>
<FONT color="green">619</FONT>             * @return size in all dimensions<a name="line.619"></a>
<FONT color="green">620</FONT>             */<a name="line.620"></a>
<FONT color="green">621</FONT>            public int[] getDimensionSizes() {<a name="line.621"></a>
<FONT color="green">622</FONT>                return dimensionSize.clone();<a name="line.622"></a>
<FONT color="green">623</FONT>            }<a name="line.623"></a>
<FONT color="green">624</FONT>    <a name="line.624"></a>
<FONT color="green">625</FONT>            /**<a name="line.625"></a>
<FONT color="green">626</FONT>             * Get the underlying storage array.<a name="line.626"></a>
<FONT color="green">627</FONT>             *<a name="line.627"></a>
<FONT color="green">628</FONT>             * @return underlying storage array<a name="line.628"></a>
<FONT color="green">629</FONT>             */<a name="line.629"></a>
<FONT color="green">630</FONT>            public Object getArray() {<a name="line.630"></a>
<FONT color="green">631</FONT>                return multiDimensionalComplexArray;<a name="line.631"></a>
<FONT color="green">632</FONT>            }<a name="line.632"></a>
<FONT color="green">633</FONT>    <a name="line.633"></a>
<FONT color="green">634</FONT>            /** {@inheritDoc} */<a name="line.634"></a>
<FONT color="green">635</FONT>            @Override<a name="line.635"></a>
<FONT color="green">636</FONT>            public Object clone() {<a name="line.636"></a>
<FONT color="green">637</FONT>                MultiDimensionalComplexMatrix mdcm =<a name="line.637"></a>
<FONT color="green">638</FONT>                        new MultiDimensionalComplexMatrix(Array.newInstance(<a name="line.638"></a>
<FONT color="green">639</FONT>                        Complex.class, dimensionSize));<a name="line.639"></a>
<FONT color="green">640</FONT>                clone(mdcm);<a name="line.640"></a>
<FONT color="green">641</FONT>                return mdcm;<a name="line.641"></a>
<FONT color="green">642</FONT>            }<a name="line.642"></a>
<FONT color="green">643</FONT>    <a name="line.643"></a>
<FONT color="green">644</FONT>            /**<a name="line.644"></a>
<FONT color="green">645</FONT>             * Copy contents of current array into mdcm.<a name="line.645"></a>
<FONT color="green">646</FONT>             *<a name="line.646"></a>
<FONT color="green">647</FONT>             * @param mdcm array where to copy data<a name="line.647"></a>
<FONT color="green">648</FONT>             */<a name="line.648"></a>
<FONT color="green">649</FONT>            private void clone(MultiDimensionalComplexMatrix mdcm) {<a name="line.649"></a>
<FONT color="green">650</FONT>    <a name="line.650"></a>
<FONT color="green">651</FONT>                int[] vector = new int[dimensionSize.length];<a name="line.651"></a>
<FONT color="green">652</FONT>                int size = 1;<a name="line.652"></a>
<FONT color="green">653</FONT>                for (int i = 0; i &lt; dimensionSize.length; i++) {<a name="line.653"></a>
<FONT color="green">654</FONT>                    size *= dimensionSize[i];<a name="line.654"></a>
<FONT color="green">655</FONT>                }<a name="line.655"></a>
<FONT color="green">656</FONT>                int[][] vectorList = new int[size][dimensionSize.length];<a name="line.656"></a>
<FONT color="green">657</FONT>                for (int[] nextVector : vectorList) {<a name="line.657"></a>
<FONT color="green">658</FONT>                    System.arraycopy(vector, 0, nextVector, 0,<a name="line.658"></a>
<FONT color="green">659</FONT>                                     dimensionSize.length);<a name="line.659"></a>
<FONT color="green">660</FONT>                    for (int i = 0; i &lt; dimensionSize.length; i++) {<a name="line.660"></a>
<FONT color="green">661</FONT>                        vector[i]++;<a name="line.661"></a>
<FONT color="green">662</FONT>                        if (vector[i] &lt; dimensionSize[i]) {<a name="line.662"></a>
<FONT color="green">663</FONT>                            break;<a name="line.663"></a>
<FONT color="green">664</FONT>                        } else {<a name="line.664"></a>
<FONT color="green">665</FONT>                            vector[i] = 0;<a name="line.665"></a>
<FONT color="green">666</FONT>                        }<a name="line.666"></a>
<FONT color="green">667</FONT>                    }<a name="line.667"></a>
<FONT color="green">668</FONT>                }<a name="line.668"></a>
<FONT color="green">669</FONT>    <a name="line.669"></a>
<FONT color="green">670</FONT>                for (int[] nextVector : vectorList) {<a name="line.670"></a>
<FONT color="green">671</FONT>                    mdcm.set(get(nextVector), nextVector);<a name="line.671"></a>
<FONT color="green">672</FONT>                }<a name="line.672"></a>
<FONT color="green">673</FONT>            }<a name="line.673"></a>
<FONT color="green">674</FONT>        }<a name="line.674"></a>
<FONT color="green">675</FONT>    }<a name="line.675"></a>




























































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